Need to Check GR Beliefs? Integrity Filter Here!

[Paige_Turner]

Being mistaken gives me the creeps because, to the extent that truth matters, it's my only tool, shield, and weapon. So I'm always looking over my shoulder, worrying that I might believe something that's not true.

Are any of these NOT true?

1. The spacetime interval is "absolute distance," because it's Lorentz invariant.
2. All events on the null cone of a point exist at zero absolute distance from each other.
3. All events on the null cone of a point exist at different 3D locations and times, but they all exist at the same 4D location.
4. In 4 dimensions, the gravity wave from an object is coincident with the object itself.
5. When you feel the moon's pull, you are not interacting with something emitted by the moon; you are interacting with the actual physical moon in your past.
6. Time is a direction you can move in, like north or left. That is, time doesn't "pass you by;" it's a dimension with a negative metric.
7. Mass is momentum in the direction of future time.
8. As we dutifully follow our geodesic, we are falling into the future at the speed of light.
9. Acceleration in N dimensions looks like rotation in N-1 dimensions.
10. You can add energy and rotate your 4D momentum vector to extend yourself (your world line) more into space and less in time. In 3D, that 4D rotation looks like acceleration and time dilation.

I also want to check GR beliefs with people who actually know the answers, but first, I have to know which, if any, of these questions makes people inexplicably angry, even if you can't explain why.

 

[PeterDonis]

The spacetime interval is "absolute distance," because it's Lorentz invariant.

What does "absolute distance" mean? If it's just another word for "spacetime interval", then obviously your statement is true, because it's a tautology. If it means something else, what? It can't mean literally what it says, since not all spacetime intervals are spacelike.

All events on the null cone of a point exist at zero absolute distance from each other.

Can't answer until you say what you mean by "absolute distance".

All events on the null cone of a point exist at different 3D locations and times, but they all exist at the same 4D location.

False. "The same 4D location" means "the same point in spacetime", and the events on the null cone of a point are not all the same point in spacetime (since an "event" is a point in spacetime, and all of the events on the null cone of a point are distinct events, not the same, hence they are distinct points in spacetime).

(This might implicitly answer the above two questions as well, depending on what you mean by "absolute distance".)

In 4 dimensions, the gravity wave from an object is coincident with the object itself.

False, for the same reason as #3 above (since I assume you are taking "the gravity wave"--the correct term is "gravitational wave"--to be traveling on a null cone).

When you feel the moon's pull, you are not interacting with something emitted by the moon; you are interacting with the actual physical moon in your past.

"Interacting" is a bad term here because it implies a two-way phenomenon, and the effect of the physical moon in your past (more precisely, in the past light cone of the point in spacetime where you are now, feeling the moon's pull) on you is one-way.

Time is a direction you can move in, like north or left. That is, time doesn't "pass you by;" it's a dimension with a negative metric.

Partially true and partially false. You can think of "time" as a direction in spacetime (or more precisely a collection of directions in spacetime, namely, all of the future timelike ones from a given point in spacetime). You can indeed move in a "time" direction--indeed you have no choice, since you are always moving through spacetime into your future, and that motion is always in a timelike direction. Whether or not you consider yourself to be just "moving in the time direction", or also moving in "space", depends on your choice of coordinates or reference frame; in your own rest frame, you are always just "moving through time into the future", nothing else.

Time is not a "dimension with a negative metric". Dimensions don't have metrics. There is only one metric, the metric of spacetime. The way "time" appears in that metric can, under certain conditions, be described as having the opposite sign to the way "space" appears in the metric, but you have to be very careful with such statements as taking them too literally or extending them too far can lead to errors.

Mass is momentum in the direction of future time.

True if you interpret it to mean "mass is the invariant length of an object's 4-momentum vector, which points in the future timelike direction in spacetime in which the object is moving".

As we dutifully follow our geodesic, we are falling into the future at the speed of light.

True in a very limited sense, the sense that we can always normalize the tangent vector to our worldline (the curve we follow through spacetime) to have length $c$ (or length $1$ in "natural" units where $c = 1$). But there are a lot of pop science books and videos that try to use this to create some more elaborate model; all of them (or at least all that I've seen and all that have been asked about in previous threads here on PF, of which there are many) are wrong. So I would characterize the staement quoted above as "true, but useless".

Acceleration in N dimensions looks like rotation in N-1 dimensions.

False as you state it. Acceleration in spacetime can be thought of as hyperbolic rotation, but it involves N dimensions, not N - 1; you have to include the "time" dimension in the rotation.

You can add energy and rotate your 4D momentum vector to extend yourself (your world line) more into space and less in time. In 3D, that 4D rotation looks like acceleration and time dilation.

False.

I also want to check GR beliefs with people who actually know the answers, but first, I have to know which, if any, of these questions makes people inexplicably angry, even if you can't explain why.

None of these questions make me "inexplicably angry". Nor do I see why that is even relevant; the only relevant thing is what is true and what is not.

A bit of advice: please stop referring to past incidents in which you have gotten negative feedback. All it does is distract from the present thread topic. Just focus on the questions you want to ask and the things you want to understand.

 

[PeterDonis]

Being mistaken gives me the creeps because, to the extent that truth matters, it's my only tool, shield, and weapon.

A bit of advice about this, at least as regards science: truths in science are not expressed in ordinary language. They are expressed in math. Any attempt to express them in ordinary language will involve some amount of distortion. Every statement you ask about suffers from this problem, though not all to the same degree. If you really want to understand the science, you need to look at the math, not statements in ordinary language. This is particularly true if you want to use truth as a tool, shield, or weapon, since that requires you to make accurate predictions, and to do that with scientific truths you need to use math.

 

[Paige_Turner]

> What does "absolute distance" mean?

Lorentz invariant.
There is no universal coordinate system "origin" for space. Wherever you go, there you are. But there is a zero coordinate for time.
What I'm going for is using "time of an event since the big bang" as an (at least partial) absolute reference frame, one that doesn't change the relative distances between things when you move.

Yes, I already know that there are no absolute (fixed, universal) IRFs. So I want to know why "clock-ticks since the Bang" can't be one: a yardstick who's length doesn't slide around like Alice in Wonderland on mushrooms.

 

[Paige_Turner]

"Interacting" is a bad term here because it implies a two-way phenomenon, and the effect of the physical moon in your past (more precisely, in the past light cone of the point in spacetime where you are now, feeling the moon's pull) on you is one-way.

Yes, and https://physics.fullerton.edu/~jimw/general/inertia/index.htm asserts that this is because gravity from our future is undetectable for exactly the same reason that (in QED) atoms don't "wiggle" when hit by EM waves from the future propagating backwards in time.
It does say that we perceive gravity from our future as inertial mass "pushing back" when we push on it.

[I submitted a different question asking if this is true.]

 

[PeterDonis]

Lorentz invariant.

Ok, then your first statement is a tautology: it works out to "the spacetime interval is Lorentz invariant, because it's Lorentz invariant".

There is no universal coordinate system "origin" for space. Wherever you go, there you are. But there is a zero coordinate for time.

Wrong.

What I'm going for is using "time of an event since the big bang" as an (at least partial) absolute reference frame, one that doesn't change the relative distances between things when you move.

You can't. See below.

I want to know why "clock-ticks since the Bang" can't be one

Because there is no such invariant.

There are "clock ticks since the Big Bang" along particular worldlines, but the number of clock ticks since the Big Bang is not the same for all worldlines; some have different numbers of ticks than others. So there is no absolute number of clock ticks since the Big Bang.

Also, this thread was supposed to be about SR, not GR; that's how you titled it. Talking about clock ticks since the Big Bang requires GR; you can't describe the universe as a whole using SR, because the spacetime of the universe as a whole is not flat. I would strongly advise getting clear about SR first, before trying to understand GR.

 

[PeterDonis]

Yes, and https://physics.fullerton.edu/~jimw/general/inertia/index.htm asserts that this is because gravity from our future is undetectable for exactly the same reason that (in QED) atoms don't "wiggle" when hit by EM waves from the future propagating backwards in time.
It does say that we perceive gravity from our future as inertial mass "pushing back" when we push on it.

[I submitted a different question asking if this is true.]

This should be discussed in the separate thread where you submitted that question.

Note, btw, that the article you reference is not a textbook or peer-reviewed paper. It is the personal opinion of a particular physicist.

 

[Nugatory]

So I want to know why "clock-ticks since the Bang" can't be one: a yardstick who's length doesn't slide around like Alice in Wonderland on mushrooms.

That's "clock ticks since the big bang" on which worldline? We have a hypothetical clock that read zer at the big bang and is now sitting under nose, and we can reasonably call that time since the big bang along the world line that clock followed since the big bang. But there are many such worldlines, the proper time along them will in general be different, and there's no reason to consider one of them a "better" yardstick than any other.

Another problem is that this time is only useful for events along the world line followed by that clock. To associate the clock reading with any time off that world line (including proper times reported by other observers doing the same thing) we need a simultaneity convention, and we can choose that quite arbitrarily.

 

[Paige_Turner]

> truths in science are not expressed in ordinary language. They are expressed in math.

Absolutely! And one reason I don't express things with mathematical precision is that I'm too lazy to learn MATHML.

The non-joke reason is that I try to explain this stuff to other people, and that REQUIRES using analogies, and no "big words." Einstein said that if you can't explain it to your grandmother, you don't understand it. Well, I am but a humble padwan, and even when I understand the math well enough to explain it that way (as with SR), I will never explain advanced concepts to civilians by using equations.

See, Feynman is my Yoda, and he never said "mass" to the common people; he said,"stuff."

 

[PeterDonis]

one reason I don't express things with mathematical precision is that I'm too lazy to learn MATHML.

Sorry, but this is not a valid excuse. (Here at PF, btw, you would use LaTeX to put math expressions into your posts; there is a "LaTeX Guide" link at the lower left of the post window.) To put it bluntly, if you're not willing to take the time to precisely express your questions in math, why should we take the time to answer them?

The non-joke reason is that I try to explain this stuff to other people, and that REQUIRES using analogies, and no "big words."

You can only do that if you understand it yourself. And if you don't understand the math, you don't understand it. Einstein himself had to take several years to learn difficult math--differential geometry--from his friend Marcel Grossman in order to come up with the Einstein Field Equation.

Also, we are not the people you're trying to explain it to. We're the people you're asking to explain it to you. And we're telling you that math should be used in that process.

Einstein said that if you can't explain it to your grandmother, you don't understand it.

Explaining it to your grandmother is not the same as using it as a tool, shield, and weapon, which is what you said you wanted. To do the latter, as I said before, you need to be able to make accurate predictions, and that means using math.

 

[Nugatory]

The non-joke reason is that I try to explain this stuff to other people, and that REQUIRES using analogies, and no "big words."

Analogies are indeed helpful, but it is pretty much categorically impossible to construct good analogies if you do not understand the math yourself.

Einstein said that if you can't explain it to your grandmother, you don't understand it.

Fair enough, but saying that you should be able to explain it without math is not the same thing as saying that you can skip the math yourself.

 

[Paige_Turner]

> And if you don't understand the math, you don't understand it.

Why do you assume I can't do SR analytically?
GR, no. And I'm learning it as fast as I can, even though tensor calculus is a MF. But I can, for example, apply Lorentz' gamma to calculate a coordinate transformation. It's just arithmetic.
But it's not necessary when explaining the twin paradox to wide-eyed curious people.
I imagine cranks and kooks probably barge in here with their "revolutionary new theory that proves Einstein wrong."
But I'm not one of them.

 

[Paige_Turner]

> Analogies are indeed helpful, but it is pretty much categorically impossible to construct good analogies if you do not understand the math.

Yes. And I do try hard to understand math. I took enough of it as a comsci major to have majored in it instead. But note that a lot of things in SR that may superficially appear to be analogies are actually literal reality. "Time dilation is really just rotation. It's just ordinary foreshortening, like the shadow of a pencil rotating on a string, except the axis of rotation is invisible" is not an analogy. It's what actually happens.

 

[PeterDonis]

Why do you assume I can't do SR analytically?

I'm not assuming anything. I'm saying that you are not using any math for the questions you are asking in this thread, and none of the reasons you have given for that look valid to me.

 

[PeterDonis]

a lot of things in SR that may superficially appear to be analogies are actually literal reality. "Time dilation is really just rotation. It's just ordinary foreshortening, like the shadow of a pencil rotating on a string, except the axis of rotation is invisible" is not an analogy. It's what actually happens.

Not with the usual meaning of "rotation", because hyperbolic rotation is not the same as ordinary rotation. There are analogies between them, but they are not the same thing.

 

[Dale]

The spacetime interval is "absolute distance," because it's Lorentz invariant.

I would not use this term. First, “absolute” has a negative connotation. It is better to use “invariant”. And “distance” implies that it is spacelike. It is better to use “interval”, but “distance” could be acceptable as long as you leave the scare-quotes.

All events on the null cone of a point exist at zero absolute distance from each other

Zero invariant interval, yes.

All events on the null cone of a point exist at different 3D locations and times, but they all exist at the same 4D location.

No. The interval is 0, but the metric has 0 interval between distinct events. This is one of the main reasons that some theorems in Riemannian geometry fail in pseudo-Riemannian geometry.

In 4 dimensions, the gravity wave from an object is coincident with the object itself.

No, same as above.

When you feel the moon's pull, you are not interacting with something emitted by the moon; you are interacting with the actual physical moon in your past.

I don’t know the distinction you are trying to make here. What experiment can you think of (even if it is not economically feasible to do) that would determine which possibility it is?

Time is a direction you can move in, like north or left. That is, time doesn't "pass you by;" it's a dimension with a negative metric.

Ok. I would say that it has a negative signature rather than negative metric.

Mass is momentum in the direction of future time.

No, that is energy. Energy is the timelike component of the four-momentum and momentum is the spacelike component. Mass is the magnitude of the four-momentum.

As we dutifully follow our geodesic, we are falling into the future at the speed of light.

This is true even for non-geodesic paths. However, it is basically unimportant. It is just the same as saying that the length of a unit vector is 1. In this case, c is the natural unit of speed.

Acceleration in N dimensions looks like rotation in N-1 dimensions.

Do you mean N+1 dimensions? If not then I don’t know what you mean by this.

You can add energy and rotate your 4D momentum vector to extend yourself (your world line) more into space and less in time. In 3D, that 4D rotation looks like acceleration and time dilation

Yes.

 

[PeterDonis]

Yes.

I don't think that statement is true. First, "add energy" is frame-dependent. Second, "more into space and less into time" is wrong: in a fixed inertial frame, increasing your speed means the spacelike and timelike components of your 4-velocity both increase. Third, the rotation in question is hyperbolic rotation, which is not the same thing as ordinary rotation (though it has some similarities).

 

[pervect]

Being mistaken gives me the creeps because, to the extent that truth matters, it's my only tool, shield, and weapon. So I'm always looking over my shoulder, worrying that I might believe something that's not true.

Are any of these NOT true?

1. The spacetime interval is "absolute distance," because it's Lorentz invariant.
2. All events on the null cone of a point exist at zero absolute distance from each other.
3. All events on the null cone of a point exist at different 3D locations and times, but they all exist at the same 4D location.
4. In 4 dimensions, the gravity wave from an object is coincident with the object itself.
5. When you feel the moon's pull, you are not interacting with something emitted by the moon; you are interacting with the actual physical moon in your past.
6. Time is a direction you can move in, like north or left. That is, time doesn't "pass you by;" it's a dimension with a negative metric.
7. Mass is momentum in the direction of future time.
8. As we dutifully follow our geodesic, we are falling into the future at the speed of light.
9. Acceleration in N dimensions looks like rotation in N-1 dimensions.
10. You can add energy and rotate your 4D momentum vector to extend yourself (your world line) more into space and less in time. In 3D, that 4D rotation looks like acceleration and time dilation.

I also want to check GR beliefs with people who actually know the answers, but first, I have to know which, if any, of these questions makes people inexplicably angry, even if you can't explain why.

I'm sure that many of my comments have been shared by others - I haven't read them all in details. Note that some of my points are specific to Special Relativity.

Re #1. I would avoid the phrase "absolute distance". It's not standard, and I think it may be confusing you. Reword #1 with "The spacetime interval is Lorentz invariant", and similarly strike all references to "absolute distance".

Re #3. This remark is one reason why I suspect that the phrase absolute distance may be confusing you. I am not aware of any source that claims events on the null cone all exist "at the same 4d location". The Lorentz interval between these events is zero, but that doesn't mean that they share the same location.

Basically, distances can be represented by positive definite quadratic forms, but the Lorentz interval is not positive definite, making it a bit different from the notion of a distance. The Lorentz interval is still a quadratic form, but it's not positive definite. So the Lorentz interval is closely related to a distance, but it's not quite the same concept. Which is where I think you may be getting confused.

The fact that two events in a 4d space-time can be different events, separated by a non-zero displacement, illustrates why the Lorentz interval is not positive definite.

You've said other things I disagree with too, but I think this is long enough for now.

 

[Paige_Turner]

> That's "clock ticks since the big bang" on which worldline?

Look,

• The interval length between any two events specified in 4D coordinates is invariant.
• If one of those events is the Bang (which absolutely is fixed in 4D), then the age of every event (seconds since BB) is invariant, too.

I'm perfectly willing to believe that this argument invalid, but I'd have to know why.

 

[Dale]

The interval length between any two events specified in 4D coordinates is invariant.

Actually, this only works in flat spacetime. The interval along any given path is invariant, but there are infinitely many paths connecting any two events. In flat spacetime you can just use the unique geodesic path between the two events as a sort of “implied” path, but that doesn’t work in curved spacetime since there can be multiple geodesics connecting two events.

 

[Paige_Turner]

> there can be multiple geodesics connecting two events.

But when i drop a ball in a gravity field, it always follows the same geodesic. Is this contradictory?

 

[PeterDonis]

• The interval length between any two events specified in 4D coordinates is invariant.

Wrong. The interval length between any two events along a particular worldline is invariant. You have to specify the worldline.

SR textbooks often obfuscate this by using the term "interval" as though it were independent of any worldline, when in fact what it actually means is "interval length along the unique geodesic curve that connects the two points". That's what the formula $s^2 = x^2 - t^2$ (or its equivalent in 4 dimensions) is giving you.

I'm perfectly willing to believe that this argument invalid, but I'd have to know why.

See above.

 

[PeterDonis]

> there can be multiple geodesics connecting two events.

But when i drop a ball in a gravity field, it always follows the same geodesic. Is this contradictory?

No. See, for example, the last paragraph of this post of mine in another thread earlier today:

https://www.physicsforums.com/threa...like-pull-on-other-stuff.1005130/post-6516006

(Note that this example talks about a ball being thrown upwards along a radial trajectory, but the connection should be clear.)

 

[Dale]

> there can be multiple geodesics connecting two events.

But when i drop a ball in a gravity field, it always follows the same geodesic. Is this contradictory?

No. Why would it be?

 

[PeterDonis]

when i drop a ball in a gravity field, it always follows the same geodesic.

More precisely, if you release a freely falling object with the same initial velocity from a given event, it always follows the same geodesic. But different initial velocities will lead to different geodesics. And some of those different geodesics will end up meeting the first geodesic again at some other event.

 

[Dale]

@Paige_Turner to expand a bit on why it is not a contradiction let me go into some detail.

On a flat surface there is exactly one geodesic connecting two points. But consider two points on a sphere, where the geodesics are great circles.

For most pairs of points on the sphere there are two geodesics, for instance two nearby points on the equator are connected by a short geodesic going one way along the equator and a long geodesic going the other way. However, antipodal points, like the north and south poles, are connected by an infinite number of equal length geodesics.

Between any pair of points, the geodesics that connect them are distinguished by the direction (tangent vector) from either point. So starting from one point on the equator the two geodesics to another point on the equator are distinguished by whether your bearing is east or west, and the geodesics from one pole to the other are distinguished by which bearing you take from the pole.

In spacetime your tangent vector includes both the spatial direction and also your speed. Objects with different speeds are simply pointing in different directions in spacetime. So with any starting event and tangent vector define a unique geodesic, but a starting event and an ending event do not.

For example, suppose you throw a ball hard enough that it does a circular orbit around a spherical non-rotating planet, there is also a specific speed that you can throw the ball radially upward such that it returns at the same time. These are two different geodesics connecting the same two events, and they are distinguished by the initial tangent vector, one horizontal at the circular orbit speed and the other vertical at some specific speed.

 

[pervect]

I wanted to make my remarks about quadratic forms a bit simpler. I will mostly skip over issues that distance is really the length of the a specific curve, which we can get away with in flat geometries because there's only one geodesic curve between any two points. Thus, we can without ambiguity, talk about the length of this unique curve as the distance. If we were doing more general geometries we'd have to be more careful, but since we're only doing flat geometries , we can be a bit more relaxed.

Consider cartesian coordinates on the (x,y) plane. Then the distance between two points is $dx^2 + dy^2$. If two points are not the same, the distance between them is always greater than zero.

Now consider inertial coordinates for a flat space-time (x,t). Furthermore, choose units such that c=1. Then the 4-d lorentz interval between two points is $dt^2 - dx^2$ or $dx^2 - dt^2$, depending on the sign convention one uses.

((Note that If the speed of light was not set to unity by a unit choice, this would become $c^2 dt^2 - dx^2$ or $dx^2 - c^2 dt^2$, but it's simpler to just set c=1, which we can do without loss of generality by a unit choice)).

The thing to focus on here is the minus sign. While the Lorentz interval is like distance in many respects, it is no longer true that if two points are different, that the Lorentz interval is non-zero.

Another point that is worth making. While knowing the Lorentz interval between two points doesn't allow you to tell the 3d distance between them, knowing the Lorentz interval between all possible pairs of points does, assuming you've chosen a particular inertial frame to measure the distance. Instead of considering the geodesic path between two points, consider two paths that connect them, one entirely spatial in a surface of constant time (according to the inertial frame you picked out), and the second path being timelike and a path with a constant location according to the chosen frame. Then the magnitude of the Lorentz interval of the first path is equal to the square of the 3d distance between them, and the magnitude of the Lorentz interval of the second path is the square of the time separation between the two events in the chosen frame.

Thus specifying the Lorentz interval between all possible points defines the 4d geometry, just as specifying the distance between all possible pairs of 3d points specifies a 3d geometry.

 

[PAllen]

> there can be multiple geodesics connecting two events.

But when i drop a ball in a gravity field, it always follows the same geodesic. Is this contradictory?

Just to be very explicit about the counterexample of two geodesics connecting two events:

Consider a planet orbiting the sun. Consider that it shoots a cannonball radially away from the sun with initial speed (relative to sun) such that it falls back to planet in the time of one orbital period of the planet. Then you have two free fall (geodesic) paths between two events, realized in a simple physical way.

Note that the radial path would be the one that maximized proper tine, while the orbital path would have non free fall trajectories with both greater and lesser proper time between meetings.